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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 135, Issue 3
  • November 2003, pp. 539-544

Additivity of bridge numbers of knots

  • JENNIFER SCHULTENS (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004103006832
  • Published online: 24 October 2003
Abstract

We provide a new proof of the following results of H. Schubert: if $K$ is a satellite knot with companion $J$ and pattern $(\skew1\hat{V}, L)$ with index $k$, then the bridge numbers satisfy the following: $b(K) \geq k \cdot (b(J))$. In addition, if $K$ is a composite knot with summands $J$ and $L$, then $b(K) = b(J) + b(L) - 1.$

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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